

A237929


Numbers n such that (i) the sum of prime divisors of n (with repetition) is one less than the sum of prime divisors (with repetition) of n+1, and (ii) n and n+1 have the same number of prime divisors (with repetition).


2



2, 9, 98, 170, 1274, 4233, 4345, 7105, 7625, 14905, 21385, 30457, 34945, 66585, 69874, 77314, 82946, 98841, 175354, 177122, 233090, 236282, 238017, 263145, 265225, 295274, 298082, 322234, 335793, 336106
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OFFSET

1,1


COMMENTS

The first term a(1)=2 is the only prime number in this sequence.


LINKS

Abhiram R Devesh, Table of n, a(n) for n = 1..96049


EXAMPLE

For n=98: prime factors = 2,7,7; sum of prime factors = 16; number of prime divisors = 3
For n+1=99: prime factors = 3,3,11; sum of prime factors = 17; number of prime divisors=3.


PROG

(Python)
## sumdivisors(n) is a function that would return the sum of prime
## divisors of n
## numdivisors(n) is a function that would return the number of prime
## divisors of n
i=2
while i < 100000:
..sdi=sumdivisors(i)
..sdip=sumdivisors(i+1)
..ndi=numdivisors(i)
..ndip=numdivisors(i+1)
..if sdi==sdip1 and ndi==ndip:
....print i, i+1
..i=i+1


CROSSREFS

Cf. A001414, A006145 RuthAaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.
Cf. A228126 Sum of prime divisors of n (with repetition) is one less than the sum of prime divisors (with repetition) of n+1.
Cf. A045920 Numbers n such that factorizations of n and n+1 have same number of primes (including multiplicities).
Sequence in context: A013132 A317275 A013057 * A227258 A027686 A360696
Adjacent sequences: A237926 A237927 A237928 * A237930 A237931 A237932


KEYWORD

nonn


AUTHOR

Abhiram R Devesh, Feb 16 2014


STATUS

approved



